Question

Find the area the sector.arc circle 9A. 275π/6 m²B. 175π/2 m²C. 18π m²D. 5π/3 m²

Answer 1

The area of a sector is expressed as

`\begin{gathered} area=(\theta)/(360)*\pi r^2 \\ where \\ \theta\Rightarrow angle\text{ subtended by the sector} \\ r\Rightarrow radius\text{ of the circle} \end{gathered}`

Given:

we see that

`\begin{gathered} \theta=165\degree \\ r=10\text{ m} \end{gathered}`

By substitution, we have

`\begin{gathered} area=(165)/(360)*\pi*10*10 \\ =(275\pi)/(6)\text{ m}^2 \end{gathered}`

Hence, the area of the sector is evaluated to be

`(275\pi)/(6)\text{ m}^2`

The correct option is A